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Mathematics of Computation

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Evaluating Jacquet's $ \mathbf{{\rm GL}(n)}$ Whittaker function

Author: Kevin A. Broughan
Journal: Math. Comp. 78 (2009), 1061-1072
MSC (2000): Primary 33C15, 22E30, 11E57, 11E76
Published electronically: August 28, 2008
MathSciNet review: 2476570
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Abstract: Algorithms for the explicit symbolic and numeric evaluation of Jacquet's Whittaker function for the $ GL(n,\mathbb{R})$ based generalized upper half-plane for $ n\ge 2$, and an implementation for symbolic evaluation in the Mathematica package GL(n)pack, are described. This requires a comparison of the different definitions of Whittaker function which have appeared in the literature.

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Additional Information

Kevin A. Broughan
Affiliation: Department of Mathematics, University of Waikato, Hamilton, New Zealand

Keywords: K-Bessel function, Whittaker function, Jacquet Whittaker function, symbolic evaluation, quadrature, unbounded domain.
Received by editor(s): November 6, 2006
Received by editor(s) in revised form: March 3, 2008
Published electronically: August 28, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.